*ICMR - Isolated Congenital Mitral Regurgitation
Theories:
Aim:
Methods used :
Descriptive Statistics
Flow chart of the study
About the data
The data set contains variables on 119 patients. The outcome variable is Cause_of_redo (qualitative information).
The data set has a total of 45 variables (after processing). Some of the predictor variables which are going to be used in the multinomial regression model are:
Data Visualization
nnet
\(\underline{Step \hspace{.05in} 1}\): Relevel the baseline groups
data$Cause_of_redo <- factor(data$Cause_of_redo, levels = c("NONE", "MR", "MS"))
data$Age_group <- factor(data$Age_group, levels = c('0-4 yrs', '5-9 yrs', '10-14 yrs', '15-18 yrs'))
data$GROUP <- factor(data$GROUP, levels = c("NONE", "BAND", "RING"))
data$Ring_Group <- factor(data$Ring_Group, levels = c("NONE", "<26", ">=26"))
\(\underline{Step \hspace{.05in} 2}\): Fit the model and obtain the results
test <- multinom(Cause_of_redo ~ Age_group + Sex + GROUP + Ring_Group, data = data)
summary(test)$coefficients
## (Intercept) Age_group5-9 yrs Age_group10-14 yrs Age_group15-18 yrs
## MR -22.48180 1.065216 -19.76857 -13.43422
## MS -21.02828 1.771954 -24.99633 -15.00068
## SexM GROUPBAND GROUPRING Ring_Group<26 Ring_Group>=26
## MR -0.5094286 20.76360 12.99527 6.434332 6.560936
## MS 0.6762916 16.64434 12.43413 7.364345 5.069786
\(\underline{Step \hspace{.05in} 3}\): Find the p-value of each coefficient
z <- summary(test)$coefficients/summary(test)$standard.errors
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
## (Intercept) Age_group5-9 yrs Age_group10-14 yrs Age_group15-18 yrs SexM
## MR 0 0.20761394 0 0.9930179 0.5758157
## MS 0 0.01816458 0 0.0000000 0.3507771
## GROUPBAND GROUPRING Ring_Group<26 Ring_Group>=26
## MR 0 0 0 4.440892e-15
## MS 0 0 0 2.220446e-16
Comment: Overall all coefficients (except for Sex variable) are statistically significant based on their p-values being smaller 0.05. The model equation for the first row is then:
\[ \scriptsize \begin{eqnarray} \text{ln}\bigg(\frac{Pr(\text{type} = \text{MR})}{Pr(\text{type = NONE})}\bigg) &= \beta_{10} + \beta_{11}(\text{age = 5-9 yrs}) + \beta_{12}(\text{age = 10-14 yrs}) + \beta_{13}(\text{age = 15-18 yrs}) + \beta_{14}(\text{Sex = M}) \\ & + \beta_{15}(\text{grp = Band}) + \beta_{16}(\text{grp = Ring}) + \beta_{17}(\text{Ring_grp = "<26"}) + \beta_{18}(\text{Ring_grp = ">=26"}) \end{eqnarray} \]
For MR patients:
The model equation for the second row is: \[
\scriptsize
\begin{eqnarray}
\text{ln}\bigg(\frac{Pr(\text{type} = \text{MS})}{Pr(\text{type = NONE})}\bigg) &= \beta_{20} + \beta_{21}(\text{age = 5-9 yrs}) + \beta_{22}(\text{age = 10-14 yrs})
+ \beta_{23}(\text{age = 15-18 yrs}) + \beta_{24}(\text{Sex = M})\\
& + \beta_{25}(\text{grp = Band}) + \beta_{26}(\text{grp = Ring})
+ \beta_{27}(\text{Ring_grp = "<26"}) + \beta_{28}(\text{Ring_grp = ">=26"})
\end{eqnarray}
\]
For MS patients:
For both MR and MS,
Relative Risk
The ratio of the probability of choosing one outcome category over the probability of choosing the baseline category is often referred as relative risk. Relative risk can be computed by taking the exponential of the intercepts from the linear equation.
exp(coef(test))
## (Intercept) Age_group5-9 yrs Age_group10-14 yrs Age_group15-18 yrs
## MR 1.722966e-10 2.901464 2.597890e-09 1.464176e-06
## MS 7.371118e-10 5.882338 1.393898e-11 3.056950e-07
## SexM GROUPBAND GROUPRING Ring_Group<26 Ring_Group>=26
## MR 0.6008388 1041156169 440324.6 622.8662 706.9329
## MS 1.9665713 16925595 251231.8 1578.6812 159.1403
survivalsurvminerMethod: Kaplan-Meier non-parametric survival estimate.
Measures of interest: time to relapse
Results
Comment :
Table of survival analysis showing the first 10 observations
| time | n.risk | n.event | n.censor | surv | upper | lower |
|---|---|---|---|---|---|---|
| 9 | 119 | 0 | 2 | 1 | 1 | 1 |
| 11 | 117 | 0 | 1 | 1 | 1 | 1 |
| 14 | 116 | 0 | 1 | 1 | 1 | 1 |
| 19 | 115 | 0 | 1 | 1 | 1 | 1 |
| 21 | 114 | 0 | 1 | 1 | 1 | 1 |
| 24 | 113 | 0 | 1 | 1 | 1 | 1 |
| 26 | 112 | 1 | 2 | 0.9911 | 1 | 0.9738 |
| 27 | 109 | 1 | 4 | 0.982 | 1 | 0.9575 |
| 31 | 104 | 0 | 2 | 0.982 | 1 | 0.9575 |
| 33 | 102 | 0 | 1 | 0.982 | 1 | 0.9575 |
Comment:
n.d. Survival Analysis Basics. STHDA. http://www.sthda.com/english/wiki/survival-analysis-basics.
n.d. MULTINOMIAL LOGISTIC REGRESSION | R DATA ANALYSIS EXAMPLES. UCLA:Statistical Consulting Group. https://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/.